'Board Block for Two' printed from http://nrich.maths.org/

How do you play?
Firstly, choose the number of pegs on your board. Take it in turns with the grown-up to add a band to the board. Bands must fit round three pegs, in other words, each must make a triangle.
A band can share a peg with other bands, but the triangles must not overlap (except along the edges and pegs).
A player loses when they cannot make a triangle on their turn.

What are the winning strategies?
Once you've mastered this game, why not play to lose? How is the game affected?

Notes for grown-ups

Harder versions: try allowing more complex shapes (e.g. triangles, quadrilaterals, pentagons...). Try increasing the number of pegs on the board.

Repeat the game, aiming to find a winning strategy, then talk together about how it was found.